赋值映射、递降方程与双上同调系列

Evaluation Map,Descent Equation and Double-Cohomological Series

本文首先讨论了规范变换群的数学结构,然后利用Bonora等人介绍的赋值映射方法推导了规范理论的递降方程,并且推广了B.Zumino关于双上同调系列的讨论,得到了一般情况下由上链的上边缘算子△和底外微分d构成的双上同调系列。

The mathematical structure of gauge transformation group is discussed. Using the methods of evaluation map introduced by L. Bonora et. al., the descent equation in gauge field is given. By improving or generalizing the idea of B. Zumino about the relationship between gauge group cocycles and differential forms, the general formula of the double-Cohomological series is obtained.